Model studies typically estimate intercontinental influence on surface ozone by perturbing emissions from a source continent and diagnosing the ozone response in the receptor continent. Since the response to perturbations is non-linear due to chemistry, conclusions drawn from different studies may depend on the magnitude of the applied perturbation. We investigate this issue for intercontinental transport between North America, Europe, and Asia with sensitivity simulations in three global chemical transport models. In each region, we decrease anthropogenic emissions of NOx and nonmethane volatile organic compounds (NMVOCs) by 20% and 100%. We find strong nonlinearity in the response to NOx perturbations outside summer, reflecting transitions in the chemical regime for ozone production. In contrast, we find no significant nonlinearity to NOx perturbations in summer or to NMVOC perturbations year-round. The relative benefit of decreasing NOx vs. NMVOC from current levels to abate intercontinental pollution increases with the magnitude of emission reductions.